Question

the degree measure of each exterior angle of a regular decagon is $5x + 1$. determine the value of $x$. enter the answer in the space provided. use numbers instead of words. $x = \square$

Explanation:

Step1: Recall exterior angle sum of polygon

The sum of the exterior angles of any polygon is \(360^\circ\). For a regular decagon, it has 10 equal exterior angles. So each exterior angle of a regular decagon is \(\frac{360^\circ}{10}=36^\circ\).

Step2: Set up equation and solve for \(x\)

We know each exterior angle is \(5x + 1\), and we found it should be \(36^\circ\). So we set up the equation:
\(5x+1 = 36\)
Subtract 1 from both sides:
\(5x=36 - 1=35\)
Divide both sides by 5:
\(x=\frac{35}{5}=7\)

Answer:

7